Death Star Energy Calculator

Why M² (not M) is the one that matters: gravitational binding energy comes from every particle in the sphere pulling on every other particle, so the interaction count itself scales with mass squared — double the mass and you roughly quadruple the energy needed to blow it apart, all else equal. R shows up in the denominator because spreading the same mass over a bigger sphere weakens its self-gravity; the 3/5 factor is just the geometry of integrating that pairwise pull over a uniform sphere instead of a point mass. Real numbers make the fiction obvious: Earth's own binding energy is about 2×10³² J — roughly 400 billion times humanity's total annual energy use — which is why a 'planet-destroying superweapon' stays squarely in science fiction no matter how efficient its beam is.

The tool's real job is to place a science-fiction feat onto a ladder of real energies — from the largest nuclear device ever tested (Tsar Bomba), up through all of humanity's yearly energy use, to the raw output of a star. The eye-opener: our Sun radiates enough energy to gravitationally unbind an Earth-sized planet roughly every week. So the quantity isn't cosmically rare — an ordinary star pours it out continuously. What's pure fiction is funnelling it into a single beam in seconds.

The very quantity you're computing, (3/5)GM²/R, was once humanity's best guess for what powers the Sun. In the 1800s Kelvin and Helmholtz proposed it shines by slowly contracting, converting its own gravitational binding energy (~7×10⁴¹ J) into light. But dividing that by the Sun's luminosity gives only a few tens of millions of years of sunlight — far too short for the geological and fossil record. The paradox stood until nuclear fusion was discovered.